Fire not rendering in 2.78?
That tutorial, as you can see here, is for 2.73, and since then the Blender UI changed a bit, you can find that option in "file=>user preferences=>system" now (it's called "compute device"). 

You could also download an old 2.73 from the Blender website, to make it easier to follow the tutorial. 

Anyway, remember:


be sure to use "cycles" render before creating the "quick smoke" setup.
save the file in order to enable the cache settings
before rendering, run the simulation from the start (frame 1) since it could need recalculations
if something in the simulation seems to be stuck after some settings change, try also to delete (and thus rebuild) the cache


Also, on the above page you can download a "finished" .blend which could help you understand better.